AP EAMCET · PHYSICS · Gravitation

The rotation of the Earth (of radius \(R\) ) about its axis speeds up to a value such that a man at latitude angle \(45^{\circ}\) feels weightlessness. The duration of a day in such a case is

A \(\pi \sqrt{\frac{R}{g}}\)
B \(\pi \sqrt{\frac{2 R}{g}}\)
C \(\frac{\pi}{2} \sqrt{\frac{R}{g}}\)
D \(\pi \sqrt{\frac{g}{R}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\pi \sqrt{\frac{2 R}{g}}\)

Step-by-step Solution

Detailed explanation

Given that, angle of latitude, \(\lambda=45^{\circ}\) We know that, the expression of gravity at latitude angle is \[ g_\lambda=g-\omega^2 R \cos ^2 \lambda \] The weight of man of mass \(m\) at this point \[ w=m g_\lambda=m\left(g-\omega^2 R \cos ^2 45^{\circ}\right) \]…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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